The lifespans of turtles in a particular zoo are normally distributed. The average turtle lives $115$ years; the standard deviation is $13.6$ years. Use the empirical rule (68-95-99.7%) to estimate the probability of a turtle living between $74.2$ and $128.6$ years.
Explanation: $115$ $101.4$ $128.6$ $87.8$ $142.2$ $74.2$ $155.8$ $99.7\%$ $68\%$ $15.85\%$ $15.85\%$ We know the lifespans are normally distributed with an average lifespan of $115$ years. We know the standard deviation is $13.6$ years, so one standard deviation below the mean is $101.4$ years and one standard deviation above the mean is $128.6$ years. Two standard deviations below the mean is $87.8$ years and two standard deviations above the mean is $142.2$ years. Three standard deviations below the mean is $74.2$ years and three standard deviations above the mean is $155.8$ years. We are interested in the probability of a turtle living between $74.2$ and $128.6$ years. The empirical rule (or the 68-95-99.7 rule) tells us that $99.7\%$ of the turtles will have lifespans within 3 standard deviations of the average lifespan. It also tells us that $68\%$ of the turtles will have lifespans within 1 standard deviation of the mean. The probability of a particular turtle living between $74.2$ and $128.6$ years is $\color{orange}{15.85\%} + {68\%}$, or $83.85\%$.